Bound states and scattered states for contraction semigroups
Abstract
Let A generate a strongly continuous contraction semigroup {T(t)} on a Hilbert space and let L be a bounded operator. If L(ζI-A)-1 is compact, then the Cesàro limit of {norm of matrix}LT(t)f{norm of matrix}2 (as t→∞) is computed for all vectors f. This limit is interpreted in terms of bound and scattered states in the context of quantum mechanical and classical wave propagation problems. © 1985 D. Reidel Publishing Company.
Publication Title
Acta Applicandae Mathematicae
Recommended Citation
Goldstein, J. (1985). Bound states and scattered states for contraction semigroups. Acta Applicandae Mathematicae, 4 (1), 93-98. https://doi.org/10.1007/BF02293492
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